Subdivision-based multilevel methods for large scale engineering simulation of thin shells

This paper presents a multilevel algorithm to accelerate the numerical solution of thin shell finite element problems described by subdivision surfaces. Subdivision surfaces have become a widely used geometric representation for general curved three dimensional boundary models and thin shells as they provide a compact and robust framework for modeling 3D geometry. More recently, the shape functions used in the subdivision surfaces framework have been proposed as candidates for use as finite element basis functions in the analysis and simulation of the mechanical deformation of thin shell structures. When coupled with standard solvers, however, such simulations do not scale well. Run time costs associated with high-resolution simulations (10⁵ degrees of freedom or more) become prohibitive. The main contribution of the paper is to show that the subdivision framework can be used for accelerating such simulations. Specifically the subdivision matrix is used as the intergrid information transfer operator in a multilevel pre-conditioner. The method described in the paper allows the practical simulation or a broad range of problems. Included examples show that the run time of the algorithm presented scales nearly linearly in time with problem size.